January 20, 2014 — Jon McLoone, International Business & Strategic Development

Rock-paper-scissors* isn’t obviously interesting to look at mathematically. The Nash-equilibrium strategy is very simple: choose equally and randomly from the three choices, and (in the long run) your opponent will not beat you (nor will you beat your opponent). Nevertheless, it’s still possible for a computer strategy to beat a human player over a long run of games.

My nine-year-old daughter showed me one solution with a Scratch program that she wrote that won every time by looking at your choice before making its decision! But I will walk you through a simple solution that wins without cheating.

I had intended to write a treatise describing the history of the hydrogen atom over the last 100 years. Unfortunately, my time is running out this year, so I will content myself instead with this much briefer blog post outlining the major events associated with Niels Bohr’s three epochal papers in 1913.

The hydrogen atom has been the most fundamental application at each level in the advancement of quantum theory. It is the only real physical system that can be solved exactly (although some might argue that this is also true for the radiation field, as an assembly of harmonic oscillators).

Last month, students in the midterm review session of Harvard’s Math 21a class received a lesson in Mathematica they would not soon forget. Professor Oliver Knill coded a 3D-animated Miley Cyrus swinging on a wrecking ball to the beat of her song (by the same name). Knill used the same principles of mathematics that his class was reviewing for the midterm—and now he just may be the coolest professor ever.

By now, most of you students are likely getting into the thick of the academic year, preparing for the first wave of exams and projects and presentations to come your way… But don’t freak out just yet! Here’s a list of Wolfram’s most recent apps and programs that might help make your life a little easier. After all, it never hurts to have a few powerful resources on your side.

What is the cost of extending a warranty for a car? I’d be interested to know, since my car broke down just past the 100,000 mile marker on a road trip through America. With Mathematica 9 comes complete functionality for reliability analysis that can help us analyze systems like cars. I thought it might be worthwhile to take Mathematica for a spin and look at how some technical systems can be modeled and analyzed.

I love Maxwell’s equations. As a freshman in college, while pondering whether to major in physics, computer science, or music, it was the beauty of these equations and the physical predictions that can be elegantly extracted from them that made me decide in favor of physics. On a more universal level, the hints in Maxwell’s equations led Einstein to write Zur Elektrodynamik bewegter Körper (“On the Electrodynamics of Moving Bodies”), more commonly known as Einstein’s first paper on the theory of relativity. The quantum version of the equations, quantum electrodynamics (QED), remains our most successful physical theory, with predictions verified to 12 decimal places. There are many reasons to love Maxwell’s equations. And with Mathematica 9′s new vector analysis functionality, exploring them has never been easier.

(This is the third post in a three-part series about electrostatic and magnetostatic problems involving sharp edges.)

In the first blog post of this series, we looked at magnetic field configurations of piecewise straight wires. In the second post, we discussed charged cubes and orbits of test particles in their electric field. Today we will look at magnetic systems, concretely, mainly at a rectangular bar magnet with uniform magnetization.

June 26, 2013 — Jon McLoone, International Business & Strategic Development

My government (I’m in the UK) recently said that children here should learn up to their 12 times table by the age of 9. Now, I always believed that the reason why I learned my 12 times table was because of the money system that the UK used to have—12 pennies in a shilling. Since that madness ended with decimalization the year after I was born, by the late 1970s when I had to learn my 12 times table, it already seemed to be an anachronistic waste of time.

I am a junkie for a good math problem. Over the weekend, I encountered such a good problem on a favorite subject of mine–probability. It’s the last problem from the article “A Mathematical Trivium” by V. I. Arnol’d, Russian Mathematical Surveys 46(1), 1991, 271–278.

It’s short enough to reproduce in its entirety: “Find the mathematical expectation of the area of the projection of a cube with edge of length 1 onto a plane with an isotropically distributed random direction of projection.” In other words, what is the average area of a cube’s shadow over all possible orientations?

This blog post explores the use of Mathematica to understand and ultimately solve the problem. It recreates how I approached the problem.